
When \(n=2\)  the sufficiency was proved by Bak [1]} for \(0<\alpha \le 3/2\) . In higher dimensions, when \(0<\alpha <\alpha ^\ast \)  for some \(\alpha ^\ast <1/2\) , the complete characterization of \(L^p- L^q\)  boundedness for \(T_\alpha \)  still remains open [2]}, [3]}, [4]}. For more on this problem we refer the reader to [4]}, where the currently widest range of \(\alpha \)  can be found. We also mention the recent result [6]} in which new Bochner–Riesz estimates with negative index associated to non-elliptic surfaces were proven.
